A method of measuring dispersion and refractive index of transparent object based on spectral fiber low coherence interferometry is proposed, in which the path length of the reference arm is changed by a step motor and the interferometric signals are measured by a CCD detector. The difference between the signals from the upper and lower surfaces of a transparent plate is found and a polynominal fitting-based method is used to find the group delay dispersion. One advantage of the method is that the value of the measured dispersion is not affected by the dispersion introduced due to the mismatch between dispersions of the sample and reference arms of the system. The accuracy of the dispersion measurement is ±0.2747×10-14fs2/mm. By placing a reflective mirror in the sample arm of the interferometer, the values of dispersion mismatch can be measured and can be employed to quantitatively compensate the system dispersion. Compared with traditional methods of measuring variation of the full width at half maximum (FWHM), the proposed method can improve the accuracy and efficiency of the dispersion compensation. The dispersion compensation accuracy achieved is ±0.019×10-12fs2.